You are Here: Home >< Maths

# eigenvectors etc. watch

1. can someone explain (in detail) eigenvectors and eigenvalues etc. to me?
Thanks.
2. (Original post by lesser weevil)
can someone explain (in detail) eigenvectors and eigenvalues etc. to me?
Thanks.
Let the matrix representing a transformation be A and let the matrix it is transforming be V.

Usually at A-Level we restrict A as being 2x2 or 3x3 and V to be a 2 or 3 dimensional column vector.

Let an eigenvalue be denoted by
We say V is an eigenvector of A and is an eigenvalue of A if AV=V, that is: the image of V under the transformation is simply a multiple of the original vector.

Eigenvalues can be calculated by solving

Once you have the eigenvalues you can calculate the eigenvector for each one by using AV=V, letting V=xi+yj+zk and hence finding a relationship between x,y and z.

I'm not sure whether that's in enough depth for you but feel free to reply with queries.
3. Thanks - Erm, can you give an example?
4. (Original post by lesser weevil)
Thanks - Erm, can you give an example?
Sure. I would try to it in latex but it would take a while for me to learn the commands and then type it, so i'll use mathtype. Give me a sec.
5. where does one get "mathtype"?
6. (Original post by lesser weevil)
where does one get "mathtype"?
Don't worry, you don't need mathtype to view the output, though a google search will bring up the website of the software if you want to use it yourself for typing math.
See the attachment for an example. You might need to 'save target as' and zoom in as it's fairly long.
Attached Images

7. thanks a lot
P6 gets my goat

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 22, 2005
The home of Results and Clearing

### 2,088

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams